In a familiar method of the kind indicated at the outset (DE 42 10 381 A1), the tool and the workpiece are controlled during the entire process sequence so that the removal of material occurs exclusively along a spiral path. Although this method makes it possible to shape the concave surface, (which already largely conforms to the finished surface of the lens), this method provides poor cutting performance. If larger amounts of material are to be removed from the workpiece, the workpiece and tool have to be moved relative to each other many times along a spiral path, which results in undesirably long machining times when manufacturing eyeglasses by prescription.